The function f is defined by f(x) = kx + 7. If the graph of f is parallel to the line y = 5x - 2, what is the value of k?

Parallel lines have equal slopes. The line $y = 5x - 2$ has slope 5, and $f(x) = kx + 7$ has slope $k$, so $k = 5$, choice B. The different intercepts, $-2$ and $7$, confirm the lines are distinct parallel lines and not the same line. Choice A ($-5$) has the slope of the opposite sign, which is a reflection, not parallel. Choice C ($-\frac{1}{5}$) is the negative reciprocal, which gives a perpendicular line. Choice D ($\frac{1}{5}$) is the plain reciprocal, which gives neither parallel nor perpendicular. Parallel means the same slope.